Numerical modeling of correlated single-electron tunneling in uniform two-d
imensional arrays of small conducting islands separated by tunnel junctions
shows the possibility of soliton-antisoliton avalanches. Though the time d
uration of any avalanche and the total charge, DeltaQ=ne, transferred acros
s the array during the avalanche are always finite in arrays with length N
larger than certain critical value N-c and large width M, the avalanche mag
nitude n may be exponentially large, resulting in particular in a giant inc
rease of shot noise. Thermal fluctuations gradually suppress the avalanche
effect. Background charge disorder may lead (in larger arrays) to a gradual
change of avalanche character and to a crossover from the avalanche-induce
d shot noise to l/f-type noise.